Should I buy or build my first gaming computer? And if so what parts should i buy?

I have never had a gaming computer before and i'm pretty much a newbie to computer hardware so I need help. I have an ASUS laptop with an intel i5 quad core processor, 4gb of ram, and intel 4000 graphics(which I heard is pretty much the worst graphics option for gaming you can get), and all I play on it is minecraft mostly(bc I don't have the specs to run games) and sometimes garrys mod. I recently bought skyrim on steam and if I run it on low graphics settings it works ok. This is my first computer and its ok, but its a laptop so I can't customize it whatsoever and put better parts in so… I want a gaming computer. So first of all, should I buy one, and change out parts eventually as I get more money? Or build my own from scratch?
If you think I should build one, I would want something like:

8gb of ram
atleast 500gb of memory, but maby 1tb
an intel i5 processor
I don't know anything about motherboards so whatever you think
As for graphics cards, Geforce gtx 740-760 whatever fits the price range
My budget- the highest I can go is probably $500 but maybe more.

Btw I want it to run games that the xbox one can run at medium to good performance. I atleast want to be able to run xbox 360 games if xbox one level games are out of the $500 price range

Build your own first time with no help? You will be responsible for incompatibility, errors, damage and it might not work first day. Who to call? Also many warranties, many support agents to deal with. You might save a little.
Buy one--one warranty, it works, one support desk. But might not be ideal for you. And costs a bit more. But it comes with an OS!

You want to build (or Buy) a machine that will play the game(s) you want:
The most demanding is:
Witcher 3: [Release Date: May 19, 2015]
-Intel CPU Core i7 3770 3,4 GHz, OR
-AMD CPU AMD FX-8350 4 GHz
-Nvidia GPU GeForce GTX 770. OR
-AMD GPU Radeon R9 290
-RAM 8GB
-OS 64-bit Windows 7 or 64-bit Windows 8 (8.1)
-DirectX 11
-HDD Space 40 GB

Average games is:
-Wndows 7/Vista/XP PC (32 or 64 bit)
-Quad-core Intel or AMD CPU processor
-4GB System RAM
-6GB free HDD (Hard disk drive) space
-DirectX 9.0c compatible NVIDIA or AMD ATI video card with 1GB of RAM: Nvidia GeForce GTX 260 or higher; ATI Radeon HD 4890 or higher
-DirectX compatible sound card

Motherboards are usually matched to the CPU. http://www.tigerdirect.com
for kits and data.

Best to find an existing ready built machine that matches the specs.
You might find one that just needs a video graphics update.